Optimal. Leaf size=27 \[ -\frac{e^{\frac{1}{x}}}{x^2}-e^{\frac{1}{x}}+\frac{e^{\frac{1}{x}}}{x} \]
[Out]
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Rubi [A] time = 0.157809, antiderivative size = 27, normalized size of antiderivative = 1., number of steps used = 7, number of rules used = 3, integrand size = 12, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.25 \[ -\frac{e^{\frac{1}{x}}}{x^2}-e^{\frac{1}{x}}+\frac{e^{\frac{1}{x}}}{x} \]
Antiderivative was successfully verified.
[In] Int[(E^x^(-1)*(1 + x))/x^4,x]
[Out]
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Rubi in Sympy [F] time = 0., size = 0, normalized size = 0. \[ \int \frac{\left (x + 1\right ) e^{\frac{1}{x}}}{x^{4}}\, dx \]
Verification of antiderivative is not currently implemented for this CAS.
[In] rubi_integrate(exp(1/x)*(1+x)/x**4,x)
[Out]
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Mathematica [A] time = 0.00798998, size = 16, normalized size = 0.59 \[ e^{\frac{1}{x}} \left (-\frac{1}{x^2}+\frac{1}{x}-1\right ) \]
Antiderivative was successfully verified.
[In] Integrate[(E^x^(-1)*(1 + x))/x^4,x]
[Out]
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Maple [A] time = 0.001, size = 18, normalized size = 0.7 \[ -{\frac{ \left ({x}^{2}-x+1 \right ){{\rm e}^{{x}^{-1}}}}{{x}^{2}}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] int(exp(1/x)*(1+x)/x^4,x)
[Out]
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Maxima [A] time = 1.42257, size = 23, normalized size = 0.85 \[ -\Gamma \left (3, -\frac{1}{x}\right ) + \Gamma \left (2, -\frac{1}{x}\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((x + 1)*e^(1/x)/x^4,x, algorithm="maxima")
[Out]
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Fricas [A] time = 0.20705, size = 23, normalized size = 0.85 \[ -\frac{{\left (x^{2} - x + 1\right )} e^{\frac{1}{x}}}{x^{2}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((x + 1)*e^(1/x)/x^4,x, algorithm="fricas")
[Out]
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Sympy [A] time = 0.080872, size = 14, normalized size = 0.52 \[ \frac{\left (- x^{2} + x - 1\right ) e^{\frac{1}{x}}}{x^{2}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(exp(1/x)*(1+x)/x**4,x)
[Out]
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GIAC/XCAS [F] time = 0., size = 0, normalized size = 0. \[ \mathit{undef} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((x + 1)*e^(1/x)/x^4,x, algorithm="giac")
[Out]